If U = {x ∈ Z : −2 ≤ x ≤ 2} and A = {x ∈ U : x² = 1}, then what is n(P(A′))?
Answer and explanation
Correct answer: 8
The universal set is U = {−2, −1, 0, 1, 2}. The condition x² = 1 gives x = −1 or x = 1, so A = {−1, 1}. Therefore, the complement relative to U is A′ = {−2, 0, 2}, which has 3 elements. A set with n elements has 2ⁿ subsets in its power set. Hence n(P(A′)) = 2³ = 8, so option B is correct. The complement must always be taken with respect to the stated universal set.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The universal set is U = {−2, −1, 0, 1, 2}. The condition x² = 1 gives x = −1 or x = 1, so A = {−1, 1}. Therefore, the complement relative to U is A′ = {−2, 0, 2}, which has 3 elements. A set with n elements has 2ⁿ subsets in its power set. Hence n(P(A′)) = 2³ = 8, so option B is correct. The complement must always be taken with respect to the stated universal set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
